# The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field

Cui Minggen^{[1]}; Zhang Yanying^{[2]}

- [1] Harbin Institute of Technology Department of Mathematics No.2 WenHua west road WeiHai, ShanDong, 264209 CHINA
- [2] Harbin Normal University Department of Information Science HeXing Road Harbin,HeiLongJiang, 150080 CHINA

Annales mathématiques Blaise Pascal (2005)

- Volume: 12, Issue: 1, page 181-193
- ISSN: 1259-1734

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topMinggen, Cui, and Yanying, Zhang. "The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field." Annales mathématiques Blaise Pascal 12.1 (2005): 181-193. <http://eudml.org/doc/10510>.

@article{Minggen2005,

abstract = {In this paper, two important geometric concepts–grapical center and width, are introduced in $p$-adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in $p$-adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on $p$-adic numbers field.},

affiliation = {Harbin Institute of Technology Department of Mathematics No.2 WenHua west road WeiHai, ShanDong, 264209 CHINA; Harbin Normal University Department of Information Science HeXing Road Harbin,HeiLongJiang, 150080 CHINA},

author = {Minggen, Cui, Yanying, Zhang},

journal = {Annales mathématiques Blaise Pascal},

language = {eng},

month = {1},

number = {1},

pages = {181-193},

publisher = {Annales mathématiques Blaise Pascal},

title = {The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field},

url = {http://eudml.org/doc/10510},

volume = {12},

year = {2005},

}

TY - JOUR

AU - Minggen, Cui

AU - Yanying, Zhang

TI - The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field

JO - Annales mathématiques Blaise Pascal

DA - 2005/1//

PB - Annales mathématiques Blaise Pascal

VL - 12

IS - 1

SP - 181

EP - 193

AB - In this paper, two important geometric concepts–grapical center and width, are introduced in $p$-adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in $p$-adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on $p$-adic numbers field.

LA - eng

UR - http://eudml.org/doc/10510

ER -

## References

top- M. G. Cui, H.M Yao, H.P Liu, The Affine Frame In $p$-adic Analysis, Annales Mathematiques Blaise Pascal 10 (2003), 297-303 Zbl1066.42501MR2031273
- M. G. Cui, On the Wavelet Transform in the field ${\mathbb{Q}}_{p}$ of p-adic numbers, Appl. Comput. Harmonic Analysis 13 (2002), 162-168 Zbl1022.42025MR1942750
- G.H Gao, M.G Cui, Calculus on the field ${\mathbb{Q}}_{p}$ of $p$-adic numbers, J. of Natural Science of Heilongjiang University 3 (2003), 15-16
- Paul R. Halmos, Measure Theory, (1965), Beijing Scientific Publishing House(Chinese Translation), Beijing
- S. V. Kozyrev, Wavelet theory as $p$-adic apectral analysis, Izv. Russ, Akad. Nauk, Ser. Math. 66 (2002), 149-158(Russian) Zbl1016.42025MR1918846
- V.S Vladimirov, I.V Volovich, E.I Zelenov, p-adic Analysis and Mathematical Physics, Internat. Math. Res. Notices 13 (2996), 6613-663 Zbl0812.46076

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